G(x)=5/5x+3

Solution for G(x)=5/5x+3 equation:

(G)=5/5G+3

We move all terms to the left:

(G)-(5/5G+3)=0


Domain of the equation: 5G+3)!=0

G∈R


We get rid of parentheses

G-5/5G-3=0

We multiply all the terms by the denominator


G*5G-3*5G-5=0

Wy multiply elements

5G^2-15G-5=0

a = 5; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·5·(-5)
Δ = 325
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{13}}{2*5}=\frac{15-5\sqrt{13}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{13}}{2*5}=\frac{15+5\sqrt{13}}{10}
$